Pursuit-evasion games encompass a wide range of planning problems with a variety of constraints on the motion of agents. We study the visibility-based variant where a pursuer is required to keep an evader in sight, while the evader is assumed to attempt to hide as soon as possible. This is particularly relevant in the context of video games where non-player characters of varying skill levels frequently chase after and attack the player. In this paper, we show that a simple dual formulation of the problem can be integrated into the traditional model to derive optimal strategies that tolerate interruptions in visibility resulting from motion among obstacles. Furthermore, using the enhanced model we propose a competitive procedure to maintain the optimal strategies in a dynamic environment where obstacles can change both shape and location. We prove the correctness of our algorithms and present results for different maps.
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